Enumeration of Small, Optimal and Near-Optimal Parity-Check Erasure Codes

James S. Plank

Technical Report CS-04-535
Department of Computer Science
University of Tennessee

November, 2004

http://www.cs.utk.edu/~plank/plank/papers/CS-04-535.html

Citation Information

Plain Text:

author          J. S. Plank
title           Enumeration of Small, Optimal and Near-Optimal Parity-Check
                Erasure Codes
number          UT-CS-04-535
institution     Department of Computer Science, University of Tennessee
month           November
year            2004
where           http://www.cs.utk.edu/~plank/plank/papers/CS-04-535.html

Bibtex:

@TECHREPORT{p:04:e,
        author = "J. S. Plank",
        title = "Enumeration of Small, Optimal and Near-Optimal Parity-Check
                Erasure Codes",
        number = "UT-CS-04-535",
        institution = "Department of Computer Science, University of Tennessee",
        month = "November",
        year = "2004",
        where = "http://www.cs.utk.edu/~plank/plank/papers/CS-04-535.html"
}

This paper is not meant for publication. Instead, it is meant as a reference for systems programmers who need these codes. It is recommended that readers view the HTML of this paper with a web browser so that they may use the browser's search features to find their desired codes quickly. Also, this will save on paper.

Users of this paper are referred to Technical Report UT-CS-04-537, entitled "Small Parity-Check Erasure Codes - Exploration and Observations," by Plank, Buchsbaum, Collins and Thomason for the details and notation that accompany this paper.

Abstract/Introduction

In this paper, we enumerate the following Low-Density, Parity-Check codes, that were generated for the paper "Small Parity-Check Erasure Codes - Exploration and Observations," by Plank, Buchsbaum, Collins and Thomason (Technical Report UT-CS-04-537):

For m=3, we present the optimal codes for n less than or equal to 50, and UB_6 codes for for n less than or equal to 1,750.
For m=4, we present the optimal codes for n less than or equal to 10, and UB_4 codes for for n less than or equal to 1,000.
For m=5, we present the optimal codes for n less than or equal to 3, and UB_2 codes for for n less than or equal to 160. Additionally, we present the best codes generated by the lambda vector for m=5 and n less than or equal to 1,000.

Notation

We specify the Tanner Graphs of these codes. There are n data bits and m coding bits. The graph is a bipartite graph with N=n+m left-hand nodes, and m right-hand nodes. We specify the graphs by using the vector of c_i node counts, as detailed in in Technical Report UT-CS-04-537. Quoting from that paper:

We introduce a new nomenclature for this derivation. We note that the N left-hand nodes of any graph may be partitioned into 2^m-1 sets, depending on the right-hand nodes to which they are connected. We label these sets C_1, ..., C_{2^m-1}, and specify that l_i is an element of C_j if and only if:

j = summation_{k = 1}^{m} 2^{k-1}E(i,k),

where E(i,k) = 1 if (l_i,r_k) is an edge in G, and E(i,k) = 0 otherwise.

Let c_i = |C_i|. Then, one may uniquely specify a graph G by the values of each c_i, rather than by nodes and edges.

Thus, we specify each graph using the values of c_i. For example, the optimal code for m=4 and n=6 is specified as:

                                The counts c_i for i:
n           Overhead  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
------ ------------- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
n=6       6.48809524  1  1  1  1  1  1  0  1  1  1  0  1  0  0  0

This means that for i = 1, 2, 3, 4, 5, 6, 8, 9, 10 and 12, c_i equals one. Otherwise, c_i equals zero. Graphically, the graph looks as depictied in Figure 1:

Figure 1: the optimal graph for n=6 and m=4. Constraint nodes are boxes, and message nodes are circles, identified by the value of i for which c_i equals one. The data bits are in white circles, and coding bits in shaded circles.

Optimal Codes for m=3 and 1 <= n <= 50

  n          Overhead  c1  c2  c3  c4  c5  c6  c7
------  ------------- --- --- --- --- --- --- ---
n=1        1.00000000   1   0   1   1   0   1   0
n=2        2.20000000   1   1   1   1   1   0   0
n=3        3.20000000   1   1   1   1   1   1   0
n=4        4.28571429   1   1   1   1   1   1   1
n=5        5.37500000   2   1   1   1   1   1   1
n=6        6.42460317   2   2   1   1   1   1   1
n=7        7.45000000   2   2   1   2   1   1   1
n=8        8.47878788   2   2   2   2   1   1   1
n=9        9.49393939   2   2   2   2   2   1   1
n=10      10.50349650   2   2   2   2   2   2   1
n=11      11.52747253   3   2   2   2   2   2   1
n=12      12.54065934   3   2   2   2   2   2   2
n=13      13.54880952   3   3   2   2   2   2   2
n=14      14.55294118   3   3   2   3   2   2   2
n=15      15.56495098   3   3   3   3   2   2   2
n=16      16.57309942   3   3   3   3   3   2   2
n=17      17.57894737   3   3   3   3   3   3   2
n=18      18.58596491   4   3   3   3   3   3   2
n=19      19.59069264   4   4   3   3   3   3   2
n=20      20.59345003   4   4   3   4   3   3   2
n=21      21.59683794   4   4   3   4   3   3   3
n=22      22.60391304   4   4   4   4   3   3   3
n=23      23.60923077   4   4   4   4   4   3   3
n=24      24.61310541   4   5   4   4   4   3   3
n=25      25.61548637   4   5   4   5   4   3   3
n=26      26.61685824   4   5   4   5   4   4   3
n=27      27.61724138   5   5   4   5   4   4   3
n=28      28.62113459   5   5   4   5   4   4   4
n=29      29.62500000   6   5   4   5   4   4   4
n=30      30.62781036   6   6   4   5   4   4   4
n=31      31.62967914   6   6   4   6   4   4   4
n=32      32.63132162   6   6   5   6   4   4   4
n=33      33.63221289   6   6   5   6   5   5   3
n=34      34.63281853   6   6   5   6   5   5   4
n=35      35.63572783   7   6   5   6   5   5   4
n=36      36.63792537   7   7   5   6   5   5   4
n=37      37.63947368   7   7   5   7   5   5   4
n=38      38.64033771   7   7   5   7   5   5   5
n=39      39.64184088   7   7   6   7   6   5   4
n=40      40.64241147   7   7   6   7   6   6   4
n=41      41.64376321   7   7   6   7   6   6   5
n=42      42.64529011   8   7   6   7   6   6   5
n=43      43.64637681   8   8   6   7   6   6   5
n=44      44.64705520   8   8   6   8   6   6   5
n=45      45.64843509   8   8   7   8   6   6   5
n=46      46.64946085   8   8   7   8   7   6   5
n=47      47.65020408   8   8   7   8   7   7   5
n=48      48.65147659   9   8   7   8   7   7   5
n=49      49.65241327   9   9   7   8   7   7   5
n=50      50.65303509   9   9   7   9   7   7   5

UB_6 Codes for m=3 and 51 <= n <= 1,750

  n          Overhead  c1  c2  c3  c4  c5  c6  c7
------  ------------- --- --- --- --- --- --- ---
n=51      51.65320110   9   9   7   9   7   7   6
n=52      52.65449463   9   9   8   9   7   7   6
n=53      53.65551948   9   9   8   9   8   7   6
n=54      54.65632262   9   9   8   9   8   8   6
n=55      55.65698730  10   9   8   9   8   8   6
n=56      56.65741795  10  10   8   9   8   8   6
n=57      57.65762712  10  10   8  10   8   8   6
n=58      58.65823840  10  10   8  10   8   8   7
n=59      59.65933369  11  10   8  10   8   8   7
n=60      60.66018651  11  11   8  10   8   8   7
n=61      61.66080229  11  11   8  10   9   8   7
n=62      62.66121795  11  11   8  11   9   8   7
n=63      63.66145833  11  11   9  11   9   8   7
n=64      64.66155934  11  11   9  11   9   9   7
n=65      65.66242318  11  11   9  11   9   9   8
n=66      66.66309119  12  11   9  11   9   9   8
n=67      67.66357934  12  12   9  11   9   9   8
n=68      68.66389642  12  12   9  12   9   9   8
n=69      69.66437514  12  12  10  12   9   9   8
n=70      70.66470513  12  12  10  12  10  10   7
n=71      71.66493891  12  12  10  12  10  10   8
n=72      72.66555103  13  12  10  12  10  10   8
n=73      73.66601233  13  13  10  12  10  10   8
n=74      74.66632946  13  13  10  13  10  10   8
n=75      75.66664914  13  13  10  13  10  10   9
n=76      76.66715563  13  13  11  13  11  10   8
n=77      77.66740506  13  13  11  13  11  11   8
n=78      78.66786217  13  13  11  13  11  11   9
n=79      79.66822117  14  13  11  13  11  11   9
n=80      80.66846247  14  14  11  13  11  11   9
n=81      81.66859074  14  14  11  14  11  11   9
n=82      82.66909318  14  14  12  14  11  11   9
n=83      83.66949384  14  14  12  14  12  11   9
n=84      84.66980518  14  14  12  14  12  12   9
n=85      85.67014775  15  14  12  14  12  12   9
n=86      86.67038850  15  15  12  14  12  12   9
n=87      87.67053115  15  15  12  15  12  12   9
n=88      88.67065070  15  15  12  15  12  12  10
n=89      89.67116579  15  15  13  15  12  12  10
n=90      90.67155495  15  15  13  16  12  12  10
n=91      91.67187640  15  15  13  16  13  12  10
n=92      92.67206589  15  16  13  16  13  12  10
n=93      93.67221445  16  16  13  16  13  12  10
n=94      94.67223956  16  16  13  16  13  13  10
n=95      95.67252262  16  16  13  16  13  13  11
n=96      96.67288709  17  16  13  16  13  13  11
n=97      97.67316636  17  17  13  16  13  13  11
n=98      98.67336334  17  17  13  17  13  13  11
n=99      99.67357989  17  17  14  17  13  13  11
n=100    100.67373099  17  17  14  17  14  13  11
n=101    101.67382375  17  17  14  17  14  14  11
n=102    102.67417049  18  17  14  17  14  14  11
n=103    103.67444191  18  18  14  17  14  14  11
n=104    104.67461017  18  18  14  17  14  14  12
n=105    105.67469974  18  18  14  18  14  14  12
n=106    106.67495181  18  18  15  18  14  14  12
n=107    107.67514595  18  18  15  18  15  14  12
n=108    108.67528797  18  18  15  18  15  15  12
n=109    109.67551334  19  18  15  18  15  15  12
n=110    110.67567568  19  19  15  18  15  15  12
n=111    111.67577683  19  19  15  19  15  15  12
n=112    112.67596039  19  19  15  19  15  15  13
n=113    113.67623688  19  19  16  19  15  15  13
n=114    114.67639257  19  19  16  19  16  16  12
n=115    115.67661237  20  19  16  19  16  16  12
n=116    116.67676823  20  19  16  19  16  16  13
n=117    117.67684328  20  20  16  19  16  16  13
n=118    118.67686645  20  20  16  20  16  16  13
n=119    119.67714402  20  20  17  20  16  16  13
n=120    120.67737423  20  20  17  20  17  16  13
n=121    121.67756123  20  20  17  20  17  17  13
n=122    122.67769315  21  20  17  20  17  17  13
n=123    123.67777675  21  21  17  20  17  17  13
n=124    124.67781327  21  21  17  21  17  17  13
n=125    125.67790354  21  21  17  21  17  17  14
n=126    126.67814198  22  21  17  21  17  17  14
n=127    127.67833091  22  22  17  21  17  17  14
n=128    128.67847164  22  22  17  22  17  17  14
n=129    129.67858859  22  22  18  22  17  17  14
n=130    130.67866752  22  22  18  22  18  17  14
n=131    131.67871170  22  22  18  22  18  18  14
n=132    132.67888627  22  22  18  22  18  18  15
n=133    133.67904757  23  22  18  22  18  18  15
n=134    134.67916607  23  23  18  22  18  18  15
n=135    135.67924282  23  23  18  23  18  18  15
n=136    136.67938693  23  23  19  23  18  18  15
n=137    137.67949640  23  23  19  23  19  18  15
n=138    138.67957403  23  23  19  23  19  19  15
n=139    139.67973443  24  23  19  23  19  19  15
n=140    140.67985566  24  24  19  23  19  19  15
n=141    141.67993861  24  24  19  24  19  19  15
n=142    142.67999558  24  24  19  24  19  19  16
n=143    143.68016060  24  24  20  24  19  19  16
n=144    144.68029396  24  24  20  24  20  19  16
n=145    145.68039804  24  24  20  24  20  20  16
n=146    146.68049915  25  24  20  24  20  20  16
n=147    147.68056594  25  25  20  24  20  20  16
n=148    148.68059914  25  25  20  25  20  20  16
n=149    149.68072499  25  25  20  25  20  20  17
n=150    150.68090041  26  25  20  25  20  20  17
n=151    151.68102073  25  25  21  25  21  21  16
n=152    152.68112406  26  25  21  25  21  21  16
n=153    153.68119569  26  26  21  25  21  21  16
n=154    154.68123627  26  26  21  26  21  21  16
n=155    155.68124647  26  26  21  26  21  21  17
n=156    156.68141913  27  26  21  26  21  21  17
n=157    157.68155053  27  26  21  26  21  21  18
n=158    158.68164186  27  27  21  26  21  21  18
n=159    159.68170290  27  27  21  27  21  21  18
n=160    160.68178275  27  27  22  27  22  21  17
n=161    161.68180458  27  27  22  27  22  22  17
n=162    162.68187667  27  27  22  27  22  22  18
n=163    163.68199984  28  27  22  27  22  22  18
n=164    164.68209430  28  28  22  27  22  22  18
n=165    165.68216064  28  28  22  28  22  22  18
n=166    166.68225088  28  28  23  28  22  22  18
n=167    167.68231813  28  28  23  28  23  22  18
n=168    168.68236393  28  28  23  28  23  23  18
n=169    169.68248694  29  28  23  28  23  23  18
n=170    170.68256793  29  28  23  28  23  23  19
n=171    171.68262288  29  29  23  28  23  23  19
n=172    172.68265270  29  29  23  29  23  23  19
n=173    173.68275974  29  29  24  29  23  23  19
n=174    174.68284540  29  29  24  29  24  23  19
n=175    175.68291105  29  29  24  29  24  24  19
n=176    176.68299414  30  29  24  29  24  24  19
n=177    177.68305331  30  30  24  29  24  24  19
n=178    178.68308898  30  30  24  30  24  24  19
n=179    179.68314006  30  30  24  30  24  24  20
n=180    180.68326083  30  30  25  30  24  24  20
n=181    181.68335970  30  30  25  31  24  24  20
n=182    182.68343511  30  30  25  31  25  24  20
n=183    183.68348559  30  31  25  31  25  24  20
n=184    184.68351912  30  31  25  31  25  25  20
n=185    185.68352486  31  31  25  31  25  25  20
n=186    186.68361968  31  31  25  31  25  25  21
n=187    187.68371786  32  31  25  31  25  25  21
n=188    188.68379413  32  32  25  31  25  25  21
n=189    189.68384886  32  32  25  32  25  25  21
n=190    190.68390194  32  32  26  32  25  25  21
n=191    191.68393782  32  32  26  32  26  25  21
n=192    192.68395755  32  32  26  32  26  26  21
n=193    193.68405649  33  32  26  32  26  26  21
n=194    194.68413486  33  33  26  32  26  26  21
n=195    195.68419301  33  33  26  33  26  26  21
n=196    196.68422871  33  33  26  33  26  26  22
n=197    197.68429648  33  33  27  33  26  26  22
n=198    198.68432461  33  33  27  33  27  27  21
n=199    199.68438451  33  33  27  33  27  27  22
n=200    200.68445317  34  33  27  33  27  27  22
n=201    201.68450313  34  34  27  33  27  27  22
n=202    202.68453471  34  34  27  34  27  27  22
n=203    203.68460810  34  34  28  34  27  27  22
n=204    204.68466610  34  34  28  34  28  27  22
n=205    205.68470955  34  34  28  34  28  28  22
n=206    206.68477994  35  34  28  34  28  28  22
n=207    207.68483271  35  35  28  34  28  28  22
n=208    208.68486814  35  35  28  35  28  28  22
n=209    209.68487883  35  35  28  35  28  28  23
n=210    210.68496364  35  35  29  35  28  28  23
n=211    211.68503394  35  35  29  35  29  28  23
n=212    212.68509050  35  35  29  35  29  29  23
n=213    213.68513548  36  35  29  35  29  29  23
n=214    214.68516435  36  36  29  35  29  29  23
n=215    215.68517736  36  36  29  36  29  29  23
n=216    216.68522282  36  36  29  36  29  29  24
n=217    217.68530453  37  36  29  36  29  29  24
n=218    218.68536991  37  37  29  36  29  29  24
n=219    219.68541919  37  37  29  37  29  29  24
n=220    220.68545501  37  37  30  37  29  29  24
n=221    221.68547806  37  37  30  37  30  29  24
n=222    222.68548900  37  37  30  37  30  30  24
n=223    223.68556469  37  37  30  37  30  30  25
n=224    224.68562265  38  37  30  37  30  30  25
n=225    225.68566562  38  38  30  37  30  30  25
n=226    226.68569380  38  38  30  38  30  30  25
n=227    227.68574141  38  38  31  38  30  30  25
n=228    228.68577692  38  38  31  38  31  30  25
n=229    229.68580093  38  38  31  38  31  31  25
n=230    230.68586065  39  38  31  38  31  31  25
n=231    231.68590613  39  39  31  38  31  31  25
n=232    232.68593759  39  39  31  39  31  31  25
n=233    233.68597187  39  39  31  39  31  31  26
n=234    234.68602969  39  39  32  39  31  31  26
n=235    235.68606026  39  39  32  39  32  32  25
n=236    236.68611147  39  39  32  39  32  32  26
n=237    237.68615086  40  39  32  39  32  32  26
n=238    238.68617713  40  40  32  39  32  32  26
n=239    239.68619046  40  40  32  40  32  32  26
n=240    240.68625142  40  40  32  40  32  32  27
n=241    241.68630306  40  40  33  40  33  32  26
n=242    242.68634334  40  40  33  40  33  33  26
n=243    243.68638490  41  40  33  40  33  33  26
n=244    244.68641397  41  41  33  40  33  33  26
n=245    245.68643072  41  41  33  41  33  33  26
n=246    246.68644645  41  41  33  41  33  33  27
n=247    247.68651626  42  41  33  41  33  33  27
n=248    248.68656727  42  41  33  41  33  34  27
n=249    249.68661102  42  42  33  41  33  34  27
n=250    250.68663860  42  42  33  41  34  34  27
n=251    251.68665774  42  42  33  42  34  34  27
n=252    252.68666324  42  42  34  42  34  34  27
n=253    253.68670391  42  42  34  42  34  34  28
n=254    254.68675541  43  42  34  42  34  34  28
n=255    255.68679517  43  43  34  42  34  34  28
n=256    256.68682336  43  43  34  43  34  34  28
n=257    257.68685774  43  43  35  43  34  34  28
n=258    258.68688271  43  43  35  43  35  34  28
n=259    259.68689871  43  43  35  43  35  35  28
n=260    260.68695151  44  43  35  43  35  35  28
n=261    261.68699311  44  44  35  43  35  35  28
n=262    262.68702039  44  44  35  43  35  35  29
n=263    263.68703362  44  44  35  44  35  35  29
n=264    264.68707650  44  44  36  44  35  35  29
n=265    265.68711041  44  44  36  44  36  35  29
n=266    266.68713573  44  44  36  44  36  36  29
n=267    267.68717256  45  44  36  44  36  36  29
n=268    268.68719898  45  45  36  44  36  36  29
n=269    269.68721511  45  45  36  45  36  36  29
n=270    270.68724731  45  45  36  45  36  36  30
n=271    271.68729770  45  45  37  45  36  36  30
n=272    272.68732844  45  45  37  45  37  37  29
n=273    273.68736688  46  45  37  45  37  37  29
n=274    274.68739535  46  46  37  45  37  37  29
n=275    275.68740804  46  46  37  45  37  37  30
n=276    276.68741104  46  46  37  46  37  37  30
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n=283    283.68761009  47  47  38  47  38  38  31
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n=328    328.68869119  55  54  44  54  44  44  36
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n=347    347.68905444  58  58  46  58  46  46  38
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n=349    349.68908314  58  58  47  58  47  46  38
n=350    350.68909005  58  58  47  58  47  47  38
n=351    351.68911936  59  58  47  58  47  47  38
n=352    352.68914255  59  59  47  58  47  47  38
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n=357    357.68922208  59  59  48  59  48  48  39
n=358    358.68924289  60  59  48  59  48  48  39
n=359    359.68925789  60  60  48  59  48  48  39
n=360    360.68926715  60  60  48  60  48  48  39
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n=367    367.68937835  61  61  49  61  49  49  40
n=368    368.68940697  61  61  50  61  49  49  40
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n=370    370.68945048  61  61  50  61  50  50  40
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n=372    372.68947366  62  62  50  61  50  50  40
n=373    373.68947730  62  62  50  62  50  50  40
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n=380    380.68958329  63  63  51  63  51  51  41
n=381    381.68960945  63  63  51  63  51  51  42
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n=383    383.68964309  64  64  51  63  51  51  42
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n=386    386.68968294  64  64  52  64  52  51  42
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n=389    389.68972807  65  65  52  64  52  52  42
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n=391    391.68975096  65  65  52  65  52  52  43
n=392    392.68977242  65  65  53  65  52  52  43
n=393    393.68978482  65  65  53  65  53  53  42
n=394    394.68980337  65  65  53  65  53  53  43
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n=397    397.68983017  66  66  53  66  53  53  43
n=398    398.68985253  66  66  53  66  53  53  44
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n=407    407.68998607  68  68  54  67  54  55  44
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n=409    409.69000388  68  68  54  68  55  55  44
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n=417    417.69009734  69  69  56  69  56  56  45
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n=421    421.69014836  70  70  56  70  56  56  46
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n=427    427.69022043  71  71  57  71  57  57  46
n=428    428.69023337  71  71  57  71  57  57  47
n=429    429.69025420  71  71  58  71  57  57  47
n=430    430.69026772  71  71  58  71  58  58  46
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n=433    433.69029891  72  71  58  72  58  58  47
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n=438    438.69036265  73  73  58  73  58  58  48
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n=440    440.69037401  73  73  59  73  59  59  47
n=441    441.69038149  73  73  59  73  59  59  48
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n=445    445.69043664  74  74  59  74  59  59  49
n=446    446.69044518  74  74  60  74  60  59  48
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n=465    465.69064084  77  77  62  77  62  62  51
n=466    466.69065837  78  77  62  77  62  62  51
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n=468    468.69068303  78  78  62  78  62  62  51
n=469    469.69069045  78  78  63  78  62  62  51
n=470    470.69069508  78  78  63  78  63  62  51
n=471    471.69069702  78  78  63  78  63  63  51
n=472    472.69071522  79  78  63  78  63  63  51
n=473    473.69073005  79  79  63  78  63  63  51
n=474    474.69073950  79  79  63  78  63  63  52
n=475    475.69074564  79  79  63  79  63  63  52
n=476    476.69075602  79  79  64  79  63  63  52
n=477    477.69076026  79  79  64  79  64  64  51
n=478    478.69076873  79  79  64  79  64  64  52
n=479    479.69078230  80  79  64  79  64  64  52
n=480    480.69079261  80  80  64  79  64  64  52
n=481    481.69079970  80  80  64  80  64  64  52
n=482    482.69081087  80  80  64  80  64  64  53
n=483    483.69082066  80  80  65  80  65  64  52
n=484    484.69082723  80  80  65  80  65  65  52
n=485    485.69084151  81  80  65  80  65  65  52
n=486    486.69085166  81  80  65  80  65  65  53
n=487    487.69085770  81  81  65  80  65  65  53
n=488    488.69086063  81  81  65  81  65  65  53
n=489    489.69087513  81  81  66  81  65  65  53
n=490    490.69088703  81  81  66  81  66  65  53
n=491    491.69089641  81  81  66  81  66  66  53
n=492    492.69090637  82  81  66  81  66  66  53
n=493    493.69091328  82  82  66  81  66  66  53
n=494    494.69091715  82  82  66  82  66  66  53
n=495    495.69092401  82  82  66  82  66  66  54
n=496    496.69094102  82  82  67  82  66  66  54
n=497    497.69095347  82  82  67  83  66  66  54
n=498    498.69096424  83  82  67  83  66  66  54
n=499    499.69097079  83  82  67  83  66  67  54
n=500    500.69097536  83  83  67  83  66  67  54
n=501    501.69097632  83  83  67  83  67  67  54
n=502    502.69098956  83  83  67  83  67  67  55
n=503    503.69100250  84  83  67  83  67  67  55
n=504    504.69101248  84  84  67  83  67  67  55
n=505    505.69101951  84  84  67  84  67  67  55
n=506    506.69102797  84  84  68  84  67  67  55
n=507    507.69103404  84  84  68  84  68  67  55
n=508    508.69103778  84  84  68  84  68  68  55
n=509    509.69105137  85  84  68  84  68  68  55
n=510    510.69106208  85  85  68  84  68  68  55
n=511    511.69106991  85  85  68  85  68  68  55
n=512    512.69107533  85  85  68  85  68  68  56
n=513    513.69108630  85  85  69  85  68  68  56
n=514    514.69109216  85  85  69  85  69  69  55
n=515    515.69110128  85  85  69  85  69  69  56
n=516    516.69111096  86  85  69  85  69  69  56
n=517    517.69111785  86  86  69  85  69  69  56
n=518    518.69112197  86  86  69  86  69  69  56
n=519    519.69113340  86  86  69  86  69  69  57
n=520    520.69114402  86  86  70  86  70  69  56
n=521    521.69115166  86  86  70  86  70  70  56
n=522    522.69116201  87  86  70  86  70  70  56
n=523    523.69116964  87  87  70  86  70  70  56
n=524    524.69117456  87  87  70  87  70  70  56
n=525    525.69117639  87  87  70  87  70  70  57
n=526    526.69119085  87  87  71  87  70  70  57
n=527    527.69120306  87  87  71  87  71  70  57
n=528    528.69121267  87  88  71  87  71  70  57
n=529    529.69121959  87  88  71  88  71  70  57
n=530    530.69122384  87  88  71  88  71  71  57
n=531    531.69122529  88  88  71  88  71  71  57
n=532    532.69123294  88  88  71  88  71  71  58
n=533    533.69124590  89  88  71  88  71  71  58
n=534    534.69125622  89  89  71  88  71  71  58
n=535    535.69126391  89  89  71  89  71  71  58
n=536    536.69127080  89  89  72  89  71  71  58
n=537    537.69127556  89  89  72  89  72  71  58
n=538    538.69127824  89  89  72  89  72  72  58
n=539    539.69129139  89  89  72  89  72  72  59
n=540    540.69130078  90  89  72  89  72  72  59
n=541    541.69130761  90  90  72  89  72  72  59
n=542    542.69131191  90  90  72  90  72  72  59
n=543    543.69132107  90  90  73  90  72  72  59
n=544    544.69132816  90  90  73  90  73  72  59
n=545    545.69133320  90  90  73  90  73  73  59
n=546    546.69134322  91  90  73  90  73  73  59
n=547    547.69135073  91  91  73  90  73  73  59
n=548    548.69135577  91  91  73  91  73  73  59
n=549    549.69136209  91  91  73  91  73  73  60
n=550    550.69137341  91  91  74  91  73  73  60
n=551    551.69138044  91  91  74  91  74  74  59
n=552    552.69138996  91  91  74  91  74  74  60
n=553    553.69139662  92  91  74  91  74  74  60
n=554    554.69140087  92  92  74  91  74  74  60
n=555    555.69140272  92  92  74  92  74  74  60
n=556    556.69141426  92  92  74  92  74  74  61
n=557    557.69142540  92  92  75  92  75  74  60
n=558    558.69143377  92  92  75  92  75  75  60
n=559    559.69144107  93  92  75  92  75  75  60
n=560    560.69144602  93  93  75  92  75  75  60
n=561    561.69144861  93  93  75  93  75  75  60
n=562    562.69145174  93  93  75  93  75  75  61
n=563    563.69146464  94  93  75  93  75  75  61
n=564    564.69147518  94  94  75  93  75  75  61
n=565    565.69148328  94  94  75  93  76  75  61
n=566    566.69148848  94  94  75  94  75  75  62
n=567    567.69149262  94  94  76  94  76  75  61
n=568    568.69149444  94  94  76  94  76  76  61
n=569    569.69150262  94  94  76  94  76  76  62
n=570    570.69151230  95  94  76  94  76  76  62
n=571    571.69151969  95  95  76  94  76  76  62
n=572    572.69152480  95  95  76  95  76  76  62
n=573    573.69153246  95  95  77  95  76  76  62
n=574    574.69153825  95  95  77  95  77  76  62
n=575    575.69154222  95  95  77  95  77  77  62
n=576    576.69155245  96  95  77  95  77  77  62
n=577    577.69156043  96  96  77  95  77  77  62
n=578    578.69156617  96  96  77  96  77  77  62
n=579    579.69156835  96  96  77  96  77  77  63
n=580    580.69157797  96  96  78  96  77  77  63
n=581    581.69158576  96  96  78  96  78  77  63
n=582    582.69159176  96  96  78  96  78  78  63
n=583    583.69159896  97  96  78  96  78  78  63
n=584    584.69160399  97  97  78  96  78  78  63
n=585    585.69160685  97  97  78  97  78  78  63
n=586    586.69161381  97  97  78  97  78  78  64
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n=1370  1370.69376014 226 226 183 226 182 182 148
n=1371  1371.69376186 226 226 183 226 183 182 148
n=1372  1372.69376325 226 226 183 226 183 183 148
n=1373  1373.69376429 227 226 183 226 183 183 148
n=1374  1374.69376494 227 227 183 226 183 183 148
n=1375  1375.69376520 227 227 183 227 183 183 148
n=1376  1376.69376651 227 227 183 227 183 183 149
n=1377  1377.69376850 228 227 183 227 183 183 149
n=1378  1378.69377010 228 228 183 227 183 183 149
n=1379  1379.69377130 228 228 183 228 183 183 149
n=1380  1380.69377225 228 228 184 228 183 183 149
n=1381  1381.69377288 228 228 184 228 184 183 149
n=1382  1382.69377319 228 228 184 228 184 184 149
n=1383  1383.69377529 229 228 184 228 184 184 149
n=1384  1384.69377683 229 228 184 228 184 184 150
n=1385  1385.69377792 229 229 184 228 184 184 150
n=1386  1386.69377862 229 229 184 229 184 184 150
n=1387  1387.69377993 229 229 185 229 184 184 150
n=1388  1388.69378081 229 229 185 229 185 185 149
n=1389  1389.69378161 229 229 185 229 185 185 150
n=1390  1390.69378320 230 229 185 229 185 185 150
n=1391  1391.69378441 230 230 185 229 185 185 150
n=1392  1392.69378524 230 230 185 230 185 185 150
n=1393  1393.69378638 230 230 185 230 185 185 151
n=1394  1394.69378793 230 230 186 230 186 185 150
n=1395  1395.69378881 230 230 186 230 186 186 150
n=1396  1396.69379046 230 230 186 230 186 186 151
n=1397  1397.69379155 231 230 186 230 186 186 151
n=1398  1398.69379226 231 231 186 230 186 186 151
n=1399  1399.69379259 231 231 186 231 186 186 151
n=1400  1400.69379445 231 231 187 231 186 186 151
n=1401  1401.69379600 231 231 187 231 187 186 151
n=1402  1402.69379724 231 231 187 231 187 187 151
n=1403  1403.69379844 232 231 187 231 187 187 151
n=1404  1404.69379928 232 232 187 231 187 187 151
n=1405  1405.69379973 232 232 187 232 187 187 151
n=1406  1406.69380039 232 232 187 232 187 187 152
n=1407  1407.69380250 233 232 187 232 187 187 152
n=1408  1408.69380412 233 232 187 232 187 188 152
n=1409  1409.69380545 233 233 187 232 187 188 152
n=1410  1410.69380636 233 233 187 232 188 188 152
n=1411  1411.69380691 233 233 187 233 188 188 152
n=1412  1412.69380712 233 233 188 233 188 188 152
n=1413  1413.69380860 233 233 188 233 188 188 153
n=1414  1414.69381022 234 233 188 233 188 188 153
n=1415  1415.69381147 234 234 188 233 188 188 153
n=1416  1416.69381234 234 234 188 234 188 188 153
n=1417  1417.69381351 234 234 189 234 188 188 153
n=1418  1418.69381437 234 234 189 234 189 188 153
n=1419  1419.69381493 234 234 189 234 189 189 153
n=1420  1420.69381666 235 234 189 234 189 189 153
n=1421  1421.69381802 235 235 189 234 189 189 153
n=1422  1422.69381901 235 235 189 235 189 189 153
n=1423  1423.69381952 235 235 189 235 189 189 154
n=1424  1424.69382103 235 235 190 235 189 189 154
n=1425  1425.69382216 235 235 190 235 190 190 153
n=1426  1426.69382316 235 235 190 235 190 190 154
n=1427  1427.69382440 236 235 190 235 190 190 154
n=1428  1428.69382529 236 236 190 235 190 190 154
n=1429  1429.69382580 236 236 190 236 190 190 154
n=1430  1430.69382713 236 236 190 236 190 190 155
n=1431  1431.69382889 236 236 191 236 191 190 154
n=1432  1432.69382998 236 236 191 236 191 191 154
n=1433  1433.69383134 237 236 191 236 191 191 154
n=1434  1434.69383233 237 237 191 236 191 191 154
n=1435  1435.69383297 237 237 191 237 191 191 154
n=1436  1436.69383302 237 237 191 237 191 191 155
n=1437  1437.69383505 237 237 192 237 191 191 155
n=1438  1438.69383671 237 237 192 238 191 191 155
n=1439  1439.69383805 237 237 192 238 192 191 155
n=1440  1440.69383897 237 238 192 238 192 191 155
n=1441  1441.69383962 237 238 192 238 192 192 155
n=1442  1442.69383980 238 238 192 238 192 192 155
n=1443  1443.69384065 238 238 192 238 192 192 156
n=1444  1444.69384240 239 238 192 238 192 192 156
n=1445  1445.69384379 239 239 192 238 192 192 156
n=1446  1446.69384483 239 239 192 239 192 192 156
n=1447  1447.69384585 239 239 193 239 192 192 156
n=1448  1448.69384659 239 239 193 239 193 192 156
n=1449  1449.69384704 239 239 193 239 193 193 156
n=1450  1450.69384868 239 239 193 239 193 193 157
n=1451  1451.69384996 240 239 193 239 193 193 157
n=1452  1452.69385089 240 240 193 239 193 193 157
n=1453  1453.69385147 240 240 193 240 193 193 157
n=1454  1454.69385283 240 240 194 240 193 193 157
n=1455  1455.69385390 240 240 194 240 194 193 157
n=1456  1456.69385469 240 240 194 240 194 194 157
n=1457  1457.69385607 241 240 194 240 194 194 157
n=1458  1458.69385711 241 241 194 240 194 194 157
n=1459  1459.69385780 241 241 194 241 194 194 157
n=1460  1460.69385852 241 241 194 241 194 194 158
n=1461  1461.69386020 241 241 195 241 194 194 158
n=1462  1462.69386154 241 241 195 241 195 195 157
n=1463  1463.69386272 241 241 195 241 195 195 158
n=1464  1464.69386365 242 241 195 241 195 195 158
n=1465  1465.69386424 242 242 195 241 195 195 158
n=1466  1466.69386448 242 242 195 242 195 195 158
n=1467  1467.69386596 242 242 195 242 195 195 159
n=1468  1468.69386773 243 242 195 242 195 195 159
n=1469  1469.69386915 243 243 195 242 195 195 159
n=1470  1470.69387022 243 243 195 243 195 195 159
n=1471  1471.69387093 243 243 196 242 196 196 158
n=1472  1472.69387129 243 243 196 243 196 196 158
n=1473  1473.69387156 243 243 196 243 196 196 159
n=1474  1474.69387343 244 243 196 243 196 196 159
n=1475  1475.69387495 244 244 196 243 196 196 159
n=1476  1476.69387608 244 244 196 243 196 196 160
n=1477  1477.69387671 244 244 196 244 196 196 160
n=1478  1478.69387766 244 244 197 244 197 196 159
n=1479  1479.69387800 244 244 197 244 197 197 159
n=1480  1480.69387903 244 244 197 244 197 197 160
n=1481  1481.69388045 245 244 197 244 197 197 160
n=1482  1482.69388153 245 245 197 244 197 197 160
n=1483  1483.69388227 245 245 197 245 197 197 160
n=1484  1484.69388349 245 245 198 245 197 197 160
n=1485  1485.69388443 245 245 198 245 198 197 160
n=1486  1486.69388510 245 245 198 245 198 198 160
n=1487  1487.69388662 246 245 198 245 198 198 160
n=1488  1488.69388780 246 246 198 245 198 198 160
n=1489  1489.69388850 246 246 198 245 198 198 161
n=1490  1490.69388880 246 246 198 246 198 198 161
n=1491  1491.69389034 246 246 199 246 198 198 161
n=1492  1492.69389160 246 246 199 246 199 198 161
n=1493  1493.69389259 246 246 199 246 199 199 161
n=1494  1494.69389367 247 246 199 246 199 199 161
n=1495  1495.69389441 247 247 199 246 199 199 161
n=1496  1496.69389483 247 247 199 247 199 199 161
n=1497  1497.69389573 247 247 199 247 199 199 162
n=1498  1498.69389757 247 247 200 247 199 199 162
n=1499  1499.69389893 247 247 200 248 199 199 162
n=1500  1500.69390012 248 247 200 248 199 199 162
n=1501  1501.69390082 248 247 200 248 199 200 162
n=1502  1502.69390132 248 248 200 248 199 200 162
n=1503  1503.69390140 248 248 200 248 200 200 162
n=1504  1504.69390302 248 248 200 248 200 200 163
n=1505  1505.69390447 249 248 200 248 200 200 163
n=1506  1506.69390558 249 249 200 248 200 200 163
n=1507  1507.69390637 249 249 200 249 200 200 163
n=1508  1508.69390729 249 249 201 249 200 200 163
n=1509  1509.69390787 249 249 201 249 201 201 162
n=1510  1510.69390835 249 249 201 249 201 201 163
n=1511  1511.69390989 250 249 201 249 201 201 163
n=1512  1512.69391110 250 250 201 249 201 201 163
n=1513  1513.69391199 250 250 201 250 201 201 163
n=1514  1514.69391276 250 250 201 250 201 201 164
n=1515  1515.69391391 250 250 202 250 202 201 163
n=1516  1516.69391447 250 250 202 250 202 202 163
n=1517  1517.69391566 250 250 202 250 202 202 164
n=1518  1518.69391678 251 250 202 250 202 202 164
n=1519  1519.69391757 251 251 202 250 202 202 164
n=1520  1520.69391805 251 251 202 251 202 202 164
n=1521  1521.69391944 251 251 203 251 202 202 164
n=1522  1522.69392057 251 251 203 251 203 202 164
n=1523  1523.69392144 251 251 203 251 203 203 164
n=1524  1524.69392265 252 251 203 251 203 203 164
n=1525  1525.69392355 252 252 203 251 203 203 164
n=1526  1526.69392412 252 252 203 252 203 203 164
n=1527  1527.69392448 252 252 203 252 203 203 165
n=1528  1528.69392617 252 252 204 252 203 203 165
n=1529  1529.69392760 252 252 204 252 204 203 165
n=1530  1530.69392874 252 253 204 252 204 203 165
n=1531  1531.69392956 252 253 204 253 204 203 165
n=1532  1532.69393004 252 253 204 253 204 204 165
n=1533  1533.69393021 253 253 204 253 204 204 165
n=1534  1534.69393127 253 253 204 253 204 204 166
n=1535  1535.69393283 254 253 204 253 204 204 166
n=1536  1536.69393408 254 254 204 253 204 204 166
n=1537  1537.69393501 254 254 204 254 204 204 166
n=1538  1538.69393582 254 254 205 254 204 204 166
n=1539  1539.69393637 254 254 205 254 205 204 166
n=1540  1540.69393667 254 254 205 254 205 205 166
n=1541  1541.69393833 255 254 205 254 205 205 166
n=1542  1542.69393957 255 254 205 254 205 205 167
n=1543  1543.69394041 255 255 205 254 205 205 167
n=1544  1544.69394093 255 255 205 255 205 205 167
n=1545  1545.69394204 255 255 206 255 205 205 167
n=1546  1546.69394284 255 255 206 255 206 206 166
n=1547  1547.69394349 255 255 206 255 206 206 167
n=1548  1548.69394474 256 255 206 255 206 206 167
n=1549  1549.69394567 256 256 206 255 206 206 167
n=1550  1550.69394629 256 256 206 256 206 206 167
n=1551  1551.69394722 256 256 206 256 206 206 168
n=1552  1552.69394856 256 256 207 256 207 206 167
n=1553  1553.69394932 256 256 207 256 207 207 167
n=1554  1554.69395066 257 256 207 256 207 207 167
n=1555  1555.69395150 257 256 207 256 207 207 168
n=1556  1556.69395203 257 257 207 256 207 207 168
n=1557  1557.69395226 257 257 207 257 207 207 168
n=1558  1558.69395381 257 257 208 257 207 207 168
n=1559  1559.69395511 257 257 208 257 208 207 168
n=1560  1560.69395616 257 257 208 257 208 208 168
n=1561  1561.69395709 258 257 208 257 208 208 168
n=1562  1562.69395772 258 258 208 257 208 208 168
n=1563  1563.69395805 258 258 208 258 208 208 168
n=1564  1564.69395859 258 258 208 258 208 208 169
n=1565  1565.69396026 259 258 208 258 208 208 169
n=1566  1566.69396162 259 259 208 258 208 208 169
n=1567  1567.69396265 259 259 208 258 209 208 169
n=1568  1568.69396338 259 259 208 259 209 208 169
n=1569  1569.69396384 259 259 209 259 209 208 169
n=1570  1570.69396406 259 259 209 259 209 209 169
n=1571  1571.69396526 259 259 209 259 209 209 170
n=1572  1572.69396653 260 259 209 259 209 209 170
n=1573  1573.69396750 260 260 209 259 209 209 170
n=1574  1574.69396817 260 260 209 260 209 209 170
n=1575  1575.69396916 260 260 210 260 209 209 170
n=1576  1576.69396991 260 260 210 260 210 209 170
n=1577  1577.69397041 260 260 210 260 210 210 170
n=1578  1578.69397177 261 260 210 260 210 210 170
n=1579  1579.69397283 261 261 210 260 210 210 170
n=1580  1580.69397360 261 261 210 261 210 210 170
n=1581  1581.69397402 261 261 210 261 210 210 171
n=1582  1582.69397529 261 261 211 261 210 210 171
n=1583  1583.69397628 261 261 211 261 211 211 170
n=1584  1584.69397710 261 261 211 261 211 211 171
n=1585  1585.69397807 262 261 211 261 211 211 171
n=1586  1586.69397875 262 262 211 261 211 211 171
n=1587  1587.69397913 262 262 211 262 211 211 171
n=1588  1588.69398021 262 262 211 262 211 211 172
n=1589  1589.69398172 262 262 212 262 212 211 171
n=1590  1590.69398266 262 262 212 262 212 212 171
n=1591  1591.69398372 263 262 212 262 212 212 171
n=1592  1592.69398449 263 263 212 262 212 212 171
n=1593  1593.69398497 263 263 212 263 212 212 171
n=1594  1594.69398502 263 263 212 263 212 212 172
n=1595  1595.69398671 263 263 213 263 212 212 172
n=1596  1596.69398802 263 263 213 264 212 212 172
n=1597  1597.69398904 264 263 212 264 212 212 173
n=1598  1598.69398975 264 264 212 264 212 212 173
n=1599  1599.69399041 264 264 213 264 213 212 172
n=1600  1600.69399054 264 264 213 264 213 213 172
n=1601  1601.69399124 264 264 213 264 213 213 173
n=1602  1602.69399262 265 264 213 264 213 213 173
n=1603  1603.69399372 265 265 213 264 213 213 173
n=1604  1604.69399452 265 265 213 265 213 213 173
n=1605  1605.69399540 265 265 214 265 213 213 173
n=1606  1606.69399605 265 265 214 265 214 213 173
n=1607  1607.69399646 265 265 214 265 214 214 173
n=1608  1608.69399779 265 265 214 265 214 214 174
n=1609  1609.69399880 266 265 214 265 214 214 174
n=1610  1610.69399952 266 266 214 265 214 214 174
n=1611  1611.69399995 266 266 214 266 214 214 174
n=1612  1612.69400110 266 266 215 266 214 214 174
n=1613  1613.69400202 266 266 215 266 215 214 174
n=1614  1614.69400270 266 266 215 266 215 215 174
n=1615  1615.69400380 267 266 215 266 215 215 174
n=1616  1616.69400461 267 267 215 266 215 215 174
n=1617  1617.69400513 267 267 215 267 215 215 174
n=1618  1618.69400572 267 267 215 267 215 215 175
n=1619  1619.69400714 267 267 216 267 215 215 175
n=1620  1620.69400831 267 267 216 267 216 216 174
n=1621  1621.69400928 267 267 216 267 216 216 175
n=1622  1622.69401000 268 267 216 267 216 216 175
n=1623  1623.69401044 268 268 216 267 216 216 175
n=1624  1624.69401060 268 268 216 268 216 216 175
n=1625  1625.69401181 268 268 216 268 216 216 176
n=1626  1626.69401322 269 268 216 268 216 216 176
n=1627  1627.69401434 269 269 216 268 216 216 176
n=1628  1628.69401518 269 269 216 269 216 216 176
n=1629  1629.69401581 269 269 217 269 216 216 176
n=1630  1630.69401617 269 269 217 269 217 217 175
n=1631  1631.69401640 269 269 217 269 217 217 176
n=1632  1632.69401789 270 269 217 269 217 217 176
n=1633  1633.69401909 270 270 217 269 217 217 176
n=1634  1634.69402002 270 270 217 270 217 217 176
n=1635  1635.69402050 270 270 217 270 217 217 177
n=1636  1636.69402135 270 270 218 270 218 217 176
n=1637  1637.69402168 270 270 218 270 218 218 176
n=1638  1638.69402253 270 270 218 270 218 218 177
n=1639  1639.69402365 271 270 218 270 218 218 177
n=1640  1640.69402449 271 271 218 270 218 218 177
n=1641  1641.69402506 271 271 218 271 218 218 177
n=1642  1642.69402610 271 271 219 271 218 218 177
n=1643  1643.69402692 271 271 219 271 219 218 177
n=1644  1644.69402751 271 271 219 271 219 219 177
n=1645  1645.69402871 272 271 219 271 219 219 177
n=1646  1646.69402964 272 272 219 271 219 219 177
n=1647  1647.69403021 272 272 219 271 219 219 178
n=1648  1648.69403043 272 272 219 272 219 219 178
n=1649  1649.69403173 272 272 220 272 219 219 178
n=1650  1650.69403280 272 272 220 272 220 219 178
n=1651  1651.69403365 272 272 220 272 220 220 178
n=1652  1652.69403450 273 272 220 272 220 220 178
n=1653  1653.69403507 273 273 220 272 220 220 178
n=1654  1654.69403538 273 273 220 273 220 220 178
n=1655  1655.69403612 273 273 220 273 220 220 179
n=1656  1656.69403762 274 273 220 273 220 220 179
n=1657  1657.69403875 274 273 220 273 220 221 179
n=1658  1658.69403969 274 274 220 273 220 221 179
n=1659  1659.69404030 274 274 220 273 221 221 179
n=1660  1660.69404068 274 274 220 274 221 221 179
n=1661  1661.69404078 274 274 221 274 221 221 179
n=1662  1662.69404212 274 274 221 274 221 221 180
n=1663  1663.69404326 275 274 221 274 221 221 180
n=1664  1664.69404414 275 275 221 274 221 221 180
n=1665  1665.69404475 275 275 221 275 221 221 180
n=1666  1666.69404555 275 275 222 275 221 221 180
n=1667  1667.69404611 275 275 222 275 222 222 179
n=1668  1668.69404650 275 275 222 275 222 222 180
n=1669  1669.69404773 276 275 222 275 222 222 180
n=1670  1670.69404869 276 276 222 275 222 222 180
n=1671  1671.69404938 276 276 222 276 222 222 180
n=1672  1672.69405002 276 276 222 276 222 222 181
n=1673  1673.69405104 276 276 223 276 223 222 180
n=1674  1674.69405154 276 276 223 276 223 223 180
n=1675  1675.69405253 276 276 223 276 223 223 181
n=1676  1676.69405341 277 276 223 276 223 223 181
n=1677  1677.69405402 277 277 223 276 223 223 181
n=1678  1678.69405438 277 277 223 277 223 223 181
n=1679  1679.69405556 277 277 224 277 223 223 181
n=1680  1680.69405653 277 277 224 277 224 223 181
n=1681  1681.69405729 277 277 224 277 224 224 181
n=1682  1682.69405825 278 277 224 277 224 224 181
n=1683  1683.69405895 278 278 224 277 224 224 181
n=1684  1684.69405938 278 278 224 278 224 224 181
n=1685  1685.69405968 278 278 224 278 224 224 182
n=1686  1686.69406111 278 278 225 278 224 224 182
n=1687  1687.69406230 278 278 225 279 224 224 182
n=1688  1688.69406323 278 278 225 279 225 224 182
n=1689  1689.69406388 278 279 225 279 225 224 182
n=1690  1690.69406431 278 279 225 279 225 225 182
n=1691  1691.69406442 279 279 225 279 225 225 182
n=1692  1692.69406529 279 279 225 279 225 225 183
n=1693  1693.69406654 280 279 225 279 225 225 183
n=1694  1694.69406753 280 280 225 279 225 225 183
n=1695  1695.69406826 280 280 225 280 225 225 183
n=1696  1696.69406897 280 280 226 280 225 225 183
n=1697  1697.69406947 280 280 226 280 226 225 183
n=1698  1698.69406975 280 280 226 280 226 226 183
n=1699  1699.69407108 281 280 226 280 226 226 183
n=1700  1700.69407211 281 280 226 280 226 226 184
n=1701  1701.69407276 281 281 226 280 226 226 184
n=1702  1702.69407316 281 281 226 281 226 226 184
n=1703  1703.69407412 281 281 227 281 226 226 184
n=1704  1704.69407485 281 281 227 281 227 227 183
n=1705  1705.69407539 281 281 227 281 227 227 184
n=1706  1706.69407638 282 281 227 281 227 227 184
n=1707  1707.69407712 282 282 227 281 227 227 184
n=1708  1708.69407760 282 282 227 282 227 227 184
n=1709  1709.69407837 282 282 227 282 227 227 185
n=1710  1710.69407955 282 282 228 282 228 227 184
n=1711  1711.69408021 282 282 228 282 228 228 184
n=1712  1712.69408128 283 282 228 282 228 228 184
n=1713  1713.69408198 283 282 228 282 228 228 185
n=1714  1714.69408239 283 283 228 282 228 228 185
n=1715  1715.69408254 283 283 228 283 228 228 185
n=1716  1716.69408386 283 283 229 283 228 228 185
n=1717  1717.69408497 283 283 229 283 229 228 185
n=1718  1718.69408587 283 283 229 283 229 229 185
n=1719  1719.69408661 284 283 229 283 229 229 185
n=1720  1720.69408710 284 284 229 283 229 229 185
n=1721  1721.69408734 284 284 229 284 229 229 185
n=1722  1722.69408778 284 284 229 284 229 229 186
n=1723  1723.69408913 285 284 229 284 229 229 186
n=1724  1724.69409022 285 285 229 284 229 229 186
n=1725  1725.69409106 285 285 229 285 229 229 186
n=1726  1726.69409168 285 285 230 285 229 229 186
n=1727  1727.69409210 285 285 230 285 230 229 186
n=1728  1728.69409232 285 285 230 285 230 230 186
n=1729  1729.69409332 285 285 230 285 230 230 187
n=1730  1730.69409433 286 285 230 285 230 230 187
n=1731  1731.69409510 286 286 230 285 230 230 187
n=1732  1732.69409562 286 286 230 286 230 230 187
n=1733  1733.69409648 286 286 231 286 230 230 187
n=1734  1734.69409713 286 286 231 286 231 230 187
n=1735  1735.69409759 286 286 231 286 231 231 187
n=1736  1736.69409868 287 286 231 286 231 231 187
n=1737  1737.69409952 287 287 231 286 231 231 187
n=1738  1738.69410012 287 287 231 287 231 231 187
n=1739  1739.69410048 287 287 231 287 231 231 188
n=1740  1740.69410157 287 287 232 287 231 231 188
n=1741  1741.69410246 287 287 232 287 232 231 188
n=1742  1742.69410314 287 287 232 287 232 232 188
n=1743  1743.69410392 288 287 232 287 232 232 188
n=1744  1744.69410444 288 288 232 287 232 232 188
n=1745  1745.69410473 288 288 232 288 232 232 188
n=1746  1746.69410562 288 288 232 288 232 232 189
n=1747  1747.69410694 288 288 233 288 232 232 189
n=1748  1748.69410776 288 288 233 288 233 233 188
n=1749  1749.69410861 289 288 233 288 233 233 188
n=1750  1750.69410921 289 289 233 288 233 233 188
n=1751  1751.69410957 289 289 233 289 233 233 188

Optimal Codes for m=4 and 1 <= n <= 10

                                The counts c_i for i:
n           Overhead  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
------ ------------- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
n=1       1.00000000  1  1  0  1  0  0  0  1  0  0  0  0  0  0  1
n=2       2.20000000  1  1  0  1  0  0  1  1  0  0  1  0  0  0  0
n=3       3.22857143  1  1  0  1  0  0  1  0  1  1  0  1  0  0  0
n=4       4.38214286  1  1  0  1  0  0  1  1  1  1  0  1  0  0  0
n=5       5.46031746  1  1  1  1  0  0  1  1  1  1  0  1  0  0  0
n=6       6.48809524  1  1  1  1  1  1  0  1  1  1  0  1  0  0  0
n=7       7.50606061  1  1  1  1  1  1  0  1  1  1  0  1  0  0  1
n=8       8.58939394  1  1  1  1  1  1  1  1  1  1  0  1  0  0  1
n=9       9.63496503  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0
n=10     10.67707293  1  2  1  1  1  1  1  1  1  1  1  1  1  0  0

UB_4 Codes for m=4 and 11 <= n <= 1000

                                The counts c_i for i:
n           Overhead  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
------ ------------- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
n=11     11.70329670  1  2  1  1  1  1  1  1  1  1  1  1  1  1  0
n=12     12.72284799  2  2  1  1  1  1  1  1  1  1  1  1  1  1  0
n=13     13.73760504  2  2  1  2  1  1  1  1  1  1  1  1  1  1  0
n=14     14.74820261  2  2  1  2  1  1  1  2  1  1  1  1  1  1  0
n=15     15.77055384  2  2  1  2  1  1  1  2  1  1  1  1  1  1  1
n=16     16.79447884  2  2  2  2  1  1  1  2  1  1  1  1  1  1  1
n=17     17.81186299  2  2  2  2  1  1  1  2  1  1  1  2  1  1  1
n=18     18.82390066  2  2  1  2  2  2  1  2  2  2  1  1  1  1  0
n=19     19.83704122  2  2  1  2  2  2  1  2  2  2  1  1  1  1  1
n=20     20.84603802  2  2  2  2  2  2  1  2  2  2  1  2  1  1  0
n=21     21.85594203  2  2  2  2  2  2  1  2  2  2  1  2  1  1  1
n=22     22.86229097  3  2  2  2  2  2  1  2  2  2  1  2  1  1  1
n=23     23.86763533  3  3  2  2  2  2  1  2  2  2  1  2  1  1  1
n=24     24.87196174  3  3  2  3  2  2  1  2  2  2  1  2  1  1  1
n=25     25.87528946  3  3  2  3  2  2  1  3  2  2  1  2  1  1  1
n=26     26.88344280  3  3  2  3  2  2  2  3  2  2  1  2  1  1  1
n=27     27.89125483  3  3  2  3  2  2  2  3  2  2  2  2  1  1  1
n=28     28.89721913  3  3  2  3  2  2  2  3  2  2  2  2  2  2  0
n=29     29.90547410  4  3  2  3  2  2  2  3  2  2  2  2  2  2  0
n=30     30.91239362  4  4  2  3  2  2  2  3  2  2  2  2  2  2  0
n=31     31.91734148  4  4  2  3  2  2  2  3  2  2  2  2  2  2  1
n=32     32.92107631  4  4  2  4  2  2  2  3  2  2  2  2  2  2  1
n=33     33.92394075  4  4  2  4  2  2  2  4  2  2  2  2  2  2  1
n=34     34.92796857  4  4  3  4  2  2  2  4  2  2  2  2  2  2  1
n=35     35.93061483  4  4  3  4  2  2  2  4  2  2  2  3  2  2  1
n=36     36.93320203  4  4  3  4  2  3  2  4  2  3  2  3  2  1  1
n=37     37.93487706  4  4  3  4  2  3  2  4  3  2  2  3  2  2  1
n=38     38.93688243  4  4  3  4  3  3  2  4  3  3  2  3  2  1  1
n=39     39.93796829  4  4  3  4  3  3  2  4  3  3  2  3  2  2  1
n=40     40.94231166  5  4  3  4  3  3  2  4  3  3  2  3  2  2  1
n=41     41.94607202  5  5  3  4  3  3  2  4  3  3  2  3  2  2  1
n=42     42.94928251  5  5  3  5  3  3  2  4  3  3  2  3  2  2  1
n=43     43.95157122  5  5  3  5  3  3  2  4  3  3  2  3  2  2  2
n=44     44.95325830  5  5  3  5  3  3  2  5  3  3  2  3  2  2  2
n=45     45.95636835  5  5  4  5  3  3  2  5  3  3  2  3  2  2  2
n=46     46.95870169  5  5  4  5  3  3  2  5  3  3  2  4  2  2  2
n=47     47.96100440  5  5  4  5  4  3  2  5  3  3  2  4  2  2  2
n=48     48.96262628  5  5  4  5  4  3  2  5  3  4  2  4  2  2  2
n=49     49.96444122  5  5  4  5  4  4  2  5  3  4  2  4  2  2  2
n=50     50.96563805  5  5  4  5  4  4  2  5  4  4  2  4  2  2  2
n=51     51.96810876  6  5  4  5  4  4  2  5  4  4  2  4  2  2  2
n=52     52.97027689  6  6  4  5  4  4  2  5  4  4  2  4  2  2  2
n=53     53.97194248  6  6  4  5  4  4  2  5  4  4  2  4  3  2  2
n=54     54.97327134  6  6  4  6  4  4  2  5  4  4  2  4  3  2  2
n=55     55.97427086  6  5  4  6  4  4  3  6  4  4  3  4  2  3  1
n=56     56.97498488  6  5  4  6  4  4  3  6  4  4  3  4  3  3  1
n=57     57.97516743  6  6  4  6  4  4  3  6  4  4  3  4  3  3  1
n=58     58.97688605  6  6  4  6  4  4  3  6  4  4  3  4  3  3  2
n=59     59.97928702  7  6  4  6  4  4  3  6  4  4  3  4  3  3  2
n=60     60.98123473  6  6  4  6  4  5  3  6  5  4  3  4  3  3  2
n=61     61.98289097  7  6  4  6  4  5  3  6  5  4  3  4  3  3  2
n=62     62.98430944  6  7  4  7  5  4  3  6  4  5  3  4  3  3  2
n=63     63.98549299  6  6  5  7  4  5  3  7  5  4  3  4  3  3  2
n=64     64.98648029  7  6  5  7  4  5  3  7  5  4  3  4  3  3  2
n=65     65.98718451  6  7  5  7  5  4  3  7  4  5  3  5  3  3  2
n=66     66.98769579  7  7  5  7  5  4  3  7  4  5  3  5  3  3  2
n=67     67.98822294  7  7  5  7  5  5  3  7  4  5  3  5  3  3  2
n=68     68.98841600  7  7  5  7  5  5  3  7  5  5  3  5  3  3  2
n=69     69.98984822  7  7  5  7  5  5  3  7  5  5  3  5  3  3  3
n=70     70.99134493  7  7  5  7  5  5  4  7  5  5  4  5  3  3  2
n=71     71.99265951  7  7  5  8  5  5  4  7  5  5  4  5  3  3  2
n=72     72.99379463  7  7  5  8  5  5  4  7  5  5  4  5  4  4  1
n=73     73.99470211  7  8  5  8  5  5  4  7  5  5  4  5  4  3  2
n=74     74.99540757  7  8  5  8  5  5  4  8  5  5  4  5  4  3  2
n=75     75.99602685  8  8  5  8  5  5  4  8  5  5  4  5  4  3  2
n=76     76.99639380  8  8  5  8  5  5  4  8  5  5  4  5  4  4  2
n=77     77.99746535  8  8  6  8  5  5  4  8  5  5  4  5  4  4  2
n=78     78.99825906  8  8  6  8  5  5  4  8  5  5  4  6  4  4  2
n=79     79.99910754  8  8  6  8  6  5  4  8  5  5  4  6  4  4  2
n=80     80.99969759  8  8  6  8  6  5  4  8  5  6  4  6  4  4  2
n=81     82.00038720  8  8  6  8  6  6  4  8  5  6  4  6  4  4  2
n=82     83.00083351  8  8  6  8  6  6  4  8  6  6  4  6  4  4  2
n=83     84.00157959  9  8  6  8  6  6  4  8  6  6  4  6  4  4  2
n=84     85.00222459  9  9  6  8  6  6  4  8  6  6  4  6  4  4  2
n=85     86.00277069  9  9  6  9  6  6  4  8  6  6  4  6  4  4  2
n=86     87.00322011  9  9  6  9  6  6  4  9  6  6  4  6  4  4  2
n=87     88.00358855  9  9  6  9  6  6  4  9  6  6  4  6  4  4  3
n=88     89.00461884  9  9  7  9  6  6  4  9  6  6  4  6  4  4  3
n=89     90.00543902  9  9  7  9  6  6  4  9  6  6  4  7  4  4  3
n=90     91.00628693  9  9  7  9  7  6  4  9  6  6  4  7  4  4  3
n=91     92.00693786  9  9  7  9  7  6  4  9  6  7  4  7  4  4  3
n=92     93.00764842  9  9  7  9  7  7  4  9  6  7  4  7  4  4  3
n=93     94.00817253  9  9  7  9  7  7  4  9  7  7  4  7  4  4  3
n=94     95.00869022 10  9  7  9  7  7  4  9  7  7  4  7  4  4  3
n=95     96.00913564 10 10  7  9  7  7  4  9  7  7  4  7  4  4  3
n=96     97.00950985 10 10  7 10  7  7  4  9  7  7  4  7  4  4  3
n=97     98.00981392 10 10  7 10  7  7  4 10  7  7  4  7  4  4  3
n=98     99.01013507 10 10  7 10  7  7  5 10  7  7  4  7  4  4  3
n=99    100.01048981 10 10  7 10  7  7  5 10  7  7  5  7  4  4  3
n=100   101.01073416 10 10  7 10  7  7  5 10  7  7  5  7  5  5  2
n=101   102.01131923 10 10  7 10  7  7  5 10  7  7  5  7  5  5  3
n=102   103.01195054 11 10  7 10  7  7  5 10  7  7  5  7  5  5  3
n=103   104.01250724 11 11  7 10  7  7  5 10  7  7  5  7  5  5  3
n=104   105.01299100 11 11  7 11  7  7  5 10  7  7  5  7  5  5  3
n=105   106.01340346 11 11  7 11  7  7  5 11  7  7  5  7  5  5  3
n=106   107.01392074 11 11  8 11  7  7  5 11  7  7  5  7  5  5  3
n=107   108.01429470 11 11  8 11  7  7  5 11  7  7  5  8  5  5  3
n=108   109.01470202 11 11  8 11  8  7  5 11  7  7  5  8  5  5  3
n=109   110.01497335 11 11  8 11  8  7  5 11  7  8  5  8  5  5  3
n=110   111.01529625 11 11  8 11  8  8  5 11  7  8  5  8  5  5  3
n=111   112.01548923 11 11  8 11  8  8  5 11  8  8  5  8  5  5  3
n=112   113.01604861 11 11  8 11  8  8  5 11  8  8  5  8  5  5  4
n=113   114.01652817 12 11  8 11  8  8  5 11  8  8  5  8  5  5  4
n=114   115.01695098 12 12  8 11  8  8  5 11  8  8  5  8  5  5  4
n=115   116.01731801 12 12  8 12  8  8  5 11  8  8  5  8  5  5  4
n=116   117.01763026 12 12  8 12  8  8  5 12  8  8  5  8  5  5  4
n=117   118.01796603 12 12  8 12  8  8  6 12  8  8  6  8  5  5  3
n=118   119.01816622 12 12  8 12  8  8  6 12  8  8  6  8  6  5  3
n=119   120.01840057 12 12  8 12  8  8  6 12  8  8  6  8  6  6  3
n=120   121.01894746 12 12  9 12  8  8  6 12  8  8  6  8  6  6  3
n=121   122.01937893 12 12  9 12  8  8  6 12  8  8  6  9  6  6  3
n=122   123.01983867 12 12  9 12  9  8  6 12  8  8  6  9  6  6  3
n=123   124.02018819 12 12  9 12  9  8  6 12  8  9  6  9  6  6  3
n=124   125.02053454 13 12  9 12  9  8  6 12  8  9  6  9  6  6  3
n=125   126.02083061 12 12  8 13  9  9  6 13  9  9  6  8  6  6  3
n=126   127.02104021 12 12  9 13  9  9  6 13  9  9  6  8  6  6  3
n=127   128.02121410 12 12  9 13  9  9  6 13  9  9  6  9  6  6  3
n=128   129.02133246 13 12  9 13  9  9  6 13  9  9  6  9  6  6  3
n=129   130.02141318 13 13  9 13  9  9  6 13  9  9  6  9  6  6  3
n=130   131.02158717 13 13  9 13  9  9  6 13  9  9  6  9  6  6  4
n=131   132.02213192 14 13  9 13  9  9  6 13  9  9  6  9  6  6  4
n=132   133.02259203 14 13  9 13  9  9  6 13  9  9  6  9  6  7  4
n=133   134.02299701 14 14  9 13  9  9  6 13  9  9  6  9  6  7  4
n=134   135.02333225 13 13 10 14  9  9  6 14  9  9  6  9  7  6  4
n=135   136.02362536 13 14 10 14  9  9  6 14  9  9  6  9  7  6  4
n=136   137.02387162 13 14  9 14  9  9  7 14  9  9  7  9  7  7  3
n=137   138.02402680 14 14  9 14  9  9  7 14  9  9  7  9  7  7  3
n=138   139.02425274 14 14  9 14 10 10  6 14  9  9  7 10  6  6  4
n=139   140.02445101 14 14 10 14 10 10  6 14  9  9  7 10  6  6  4
n=140   141.02455586 14 14 10 14 10 10  6 14 10 10  6 10  6  6  4
n=141   142.02475534 14 14 10 14 10 10  6 14 10 10  6 10  6  6  5
n=142   143.02499725 14 14 10 14 10 10  7 14 10 10  7 10  6  6  4
n=143   144.02521988 14 14 10 14 10 10  7 14 10 10  7 10  7  7  3
n=144   145.02551325 14 14 10 14 10 10  7 14 10 10  7 10  7  7  4
n=145   146.02573032 15 14 10 14 10 10  7 14 10 10  7 10  7  7  4
n=146   147.02591497 15 15 10 14 10 10  7 14 10 10  7 10  7  7  4
n=147   148.02606764 15 15 10 15 10 10  7 14 10 10  7 10  7  7  4
n=148   149.02618877 15 15 10 15 10 10  7 15 10 10  7 10  7  7  4
n=149   150.02651832 15 15 11 15 10 10  7 15 10 10  7 10  7  7  4
n=150   151.02677433 15 15 11 15 10 10  7 15 10 10  7 11  7  7  4
n=151   152.02704964 15 15 11 15 11 10  7 15 10 10  7 11  7  7  4
n=152   153.02725409 15 15 11 15 11 10  7 15 10 11  7 11  7  7  4
n=153   154.02748451 15 15 11 15 11 11  7 15 10 11  7 11  7  7  4
n=154   155.02764640 15 15 11 15 11 11  7 15 11 11  7 11  7  7  4
n=155   156.02789347 16 15 11 15 11 11  7 15 11 11  7 11  7  7  4
n=156   157.02811164 16 15 11 15 11 11  7 15 11 11  7 11  7  7  5
n=157   158.02825293 16 16 11 15 11 11  7 15 11 11  7 11  7  7  5
n=158   159.02836783 16 16 11 16 11 11  7 15 11 11  7 11  7  7  5
n=159   160.02845664 16 16 11 16 11 11  7 16 11 11  7 11  7  7  5
n=160   161.02868782 16 16 11 16 11 11  8 16 11 11  7 11  7  7  5
n=161   162.02887382 16 16 11 16 11 11  8 16 11 11  8 11  8  7  4
n=162   163.02904355 16 16 11 16 11 11  8 16 11 11  8 11  8  8  4
n=163   164.02933554 17 16 11 16 11 11  8 16 11 11  8 11  8  8  4
n=164   165.02959860 17 17 11 16 11 11  8 16 11 11  8 11  8  8  4
n=165   166.02983313 17 17 11 17 11 11  8 16 11 11  8 11  8  8  4
n=166   167.03003635 17 17 11 17 11 11  8 16 11 11  8 11  8  8  5
n=167   168.03017490 17 17 11 17 11 11  8 17 11 11  8 11  8  8  5
n=168   169.03034388 17 17 11 17 11 12  8 17 12 11  8 11  8  8  4
n=169   170.03046816 17 17 11 17 11 12  8 17 12 11  8 11  8  8  5
n=170   171.03057060 17 17 11 17 12 12  8 17 12 12  8 11  8  8  4
n=171   172.03067895 17 17 12 17 12 12  8 17 12 12  8 11  8  8  4
n=172   173.03073268 17 17 12 17 12 12  8 17 12 12  8 12  8  8  4
n=173   174.03083458 17 17 12 17 12 12  8 17 12 12  8 12  8  8  5
n=174   175.03107802 18 17 12 17 12 12  8 17 12 12  8 12  8  8  5
n=175   176.03129714 18 18 12 17 12 12  8 17 12 12  8 12  8  8  5
n=176   177.03149224 18 18 12 18 12 12  8 17 12 12  8 12  8  8  5
n=177   178.03166361 18 18 12 18 12 12  8 18 12 12  8 12  8  8  5
n=178   179.03181380 18 18 12 18 12 12  9 18 12 12  8 12  8  8  5
n=179   180.03197532 18 18 12 18 12 12  9 18 12 12  9 12  8  8  5
n=180   181.03211987 18 18 12 18 12 12  9 18 12 12  9 13  8  8  5
n=181   182.03228885 18 18 12 18 12 12  9 18 13 13  8 13  8  8  5
n=182   183.03244956 18 18 13 18 12 12  9 18 13 13  8 13  8  8  5
n=183   184.03256629 18 18 13 18 13 13  8 18 13 13  8 13  8  8  5
n=184   185.03268708 18 18 13 18 13 13  8 18 13 13  8 13  8  8  6
n=185   186.03288780 19 18 13 18 13 13  8 18 13 13  8 13  8  8  6
n=186   187.03304857 19 18 13 18 13 13  9 18 13 13  8 13  8  9  5
n=187   188.03318347 19 18 13 18 13 13  9 18 13 13  9 13  8  9  5
n=188   189.03327844 19 18 13 19 13 13  9 18 13 13  9 13  8  9  5
n=189   190.03335475 19 18 13 19 13 13  9 19 13 13  9 13  8  9  5
n=190   191.03341807 19 18 13 19 13 13  9 19 13 13  9 13  9  9  5
n=191   192.03343566 19 19 13 19 13 13  9 19 13 13  9 13  9  9  5
n=192   193.03365543 19 19 13 19 13 13  9 19 13 13  9 13  9  9  6
n=193   194.03386812 19 19 13 19 13 14  9 19 14 13  9 13  9  9  5
n=194   195.03407449 19 19 14 19 13 14  9 19 14 13  9 13  9  9  5
n=195   196.03423749 19 19 14 19 13 14  9 19 14 13  9 14  9  9  5
n=196   197.03439639 20 19 14 19 13 14  9 19 14 13  9 14  9  9  5
n=197   198.03452336 19 19 14 20 14 13  9 20 13 14  9 13  9  9  6
n=198   199.03463366 20 19 14 20 14 13  9 20 13 14  9 13  9  9  6
n=199   200.03471156 19 20 14 20 13 14  9 20 14 13  9 14  9  9  6
n=200   201.03477047 20 20 14 20 13 14  9 20 14 13  9 14  9  9  6
n=201   202.03482792 20 20 14 20 14 14  9 20 14 13  9 14  9  9  6
n=202   203.03484780 20 20 14 20 14 14  9 20 14 14  9 14  9  9  6
n=203   204.03501900 20 20 14 20 14 14 10 20 14 14  9 14  9  9  6
n=204   205.03518627 20 20 14 20 14 14 10 20 14 14 10 14 10  9  5
n=205   206.03531869 20 20 14 20 14 14 10 20 14 14 10 14 10 10  5
n=206   207.03545399 21 20 14 20 14 14 10 20 14 14 10 14 10 10  5
n=207   208.03557271 21 21 14 20 14 14 10 20 14 14 10 14 10 10  5
n=208   209.03567502 21 21 14 21 14 14 10 20 14 14 10 14 10 10  5
n=209   210.03576110 21 21 14 21 14 14 10 21 14 14 10 14 10 10  5
n=210   211.03585015 21 21 14 21 14 14 10 21 14 14 10 14 10 10  6
n=211   212.03599393 21 21 15 21 14 14 10 21 14 14 10 14 10 10  6
n=212   213.03610237 21 21 15 21 14 14 10 21 14 14 10 15 10 10  6
n=213   214.03622098 21 21 15 21 15 14 10 21 14 14 10 15 10 10  6
n=214   215.03630514 21 21 15 21 15 14 10 21 14 15 10 15 10 10  6
n=215   216.03639773 21 21 15 21 15 15 10 21 15 15 10 15 10 10  5
n=216   217.03646506 21 21 15 21 15 15 10 21 15 15 10 15 10 10  6
n=217   218.03657806 22 21 15 21 15 15 10 21 15 15 10 15 10 10  6
n=218   219.03667662 22 22 15 21 15 15 10 21 15 15 10 15 10 10  6
n=219   220.03676088 22 22 15 22 15 15 10 21 15 15 10 15 10 10  6
n=220   221.03683096 22 22 15 22 15 15 10 22 15 15 10 15 10 10  6
n=221   222.03693408 22 22 15 22 15 15 10 22 15 15 10 15 10 10  7
n=222   223.03708068 22 22 15 22 15 15 11 22 15 15 11 15 10 10  6
n=223   224.03720434 22 22 15 22 15 15 11 22 15 15 11 16 10 10  6
n=224   225.03735146 22 22 15 22 15 15 11 22 16 16 10 16 10 10  6
n=225   226.03747383 22 22 15 22 16 16 10 22 16 16 10 15 10 10  7
n=226   227.03759185 22 22 16 22 16 16 10 22 16 16 10 15 10 10  7
n=227   228.03767956 22 22 16 22 16 16 10 22 16 16 10 16 10 10  7
n=228   229.03777211 23 22 16 22 16 16 10 22 16 16 10 16 10 10  7
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